Geodesic
Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method
Applications of Mathematics, Tome 51 (2006) no. 1, pp. 73-88

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By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally, numerical experiments are reported.
DOI : 10.1007/s10492-006-0006-x
Classification : 35Q30, 65N25, 65N30, 76D07
Keywords: eigenvalue problem; Stokes problem; stream function-vorticity-pressure method; asymptotic expansion; extrapolation; a posteriori error estimates 
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     title = {Approximation of an eigenvalue problem associated with the {Stokes} problem by the stream function-vorticity-pressure method},
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Chen, Wei; Lin, Qun. Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method. Applications of Mathematics, Tome 51 (2006) no. 1, pp. 73-88. doi: 10.1007/s10492-006-0006-x

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